What is the value of $$\int_{-1}^{t} \left(\frac{3}{2} - 2 \, |x| \right) \,dx? $$ I get confused integrating with the absolute value.
I forgot to mention $t>0$.
2026-03-25 20:52:47.1774471967
Value of $\int_{-1}^{t} (1.5-2|x|)\,dx$
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Hint: The only way to integrate an expression involving $|x|$ is to break it into integrals over intervals where $x$ is positive and where it is negative, then replace $|x|$ by $x$ in the first case and by $(-x)$ in the second.